TR-2003-02

On the maximum even factor in weakly symmetric graphs

Abstract

As a common generalization of matchings and matroid intersection,
W.H. Cunningham and J.F. Geelen introduced the notion of
path-matchings,
then they introduced the more general notion of
even factor in weakly symmetric digraphs.
Here we give a min-max formula for the maximum
cardinality of an even factor. Our proof is purely combinatorial. We also
provide a Gallai-Edmonds-type structure theorem for even factors.